神經網絡的收斂標準有最優值嗎?

作一個5分類的三層網絡,分類9*9的圖片,收斂標準從0.5到6e-8,共47個收斂標準,每個收斂標準收斂199次,共收斂了47*199次。取平均值統計平均性能pave。觀察pave是如何隨着收斂標準改變的。

 

得到的表格

f2[0]

f2[1]

f2[2]

f2[3]

f2[4]

迭代次數n

平均準確率p-ave

δ

耗時ms/次

耗時ms/199次

耗時 min/199

最大值p-max

平均值標準差

0.4854799

0.1858553

0.272492

0.2602853

0.2563134

1084.7739

0.6110079

0.5

70.015075

13949

0.2324833

0.8237011

0.2530133

0.5326435

0.12101

0.1954744

0.1860563

0.1582058

1643.7136

0.778164

0.4

78.79397

15680

0.2613333

0.8505546

0.0234568

0.6958971

0.0446005

0.1856664

0.1821425

0.1503321

1914.8794

0.8280271

0.3

83.59799

16654

0.2775667

0.8669002

0.0191745

0.7952586

0.0322357

0.1595491

0.1555259

0.1254544

2235.7487

0.8500412

0.2

89.135678

17738

0.2956333

0.8898618

0.0184869

0.3876615

0.0156595

0.0816177

0.0503286

0.5872436

3160.2261

0.8985676

0.1

104.77387

20850

0.3475

0.9208017

0.0088857

0.0611409

0.0047451

0.0363387

0.0046498

0.9119949

6747.4322

0.9403243

0.01

166.92462

33218

0.5536333

0.9453201

0.0018007

0.3821803

4.17E-04

0.0911098

0.0609155

0.4675613

28730.467

0.9551943

0.001

550.80905

109626

1.8271

0.9620549

0.004127

0.3118726

3.98E-04

0.1211546

0.0457933

0.5227548

31145.402

0.9568312

9.00E-04

587.94975

117033

1.95055

0.9624441

0.0036683

0.2867465

3.69E-04

0.1261143

0.0858857

0.5026527

34822.437

0.9582198

8.00E-04

644.41709

128254

2.1375667

0.963417

0.0029477

0.3319181

3.20E-04

0.1361159

0.0406462

0.4925607

39842.181

0.9591331

7.00E-04

738.93467

147048

2.4508

0.96439

0.002471

0.3067792

2.99E-04

0.1159715

0.0656649

0.5126319

45219.985

0.9600444

6.00E-04

814.98995

162229

2.7038167

0.9657521

0.0024014

0.3268212

2.69E-04

0.1209193

0.0756559

0.4774668

53172.774

0.9615122

5.00E-04

951.00503

189281

3.1546833

0.9675034

0.0029077

0.251422

0.0052492

0.1811337

0.0605513

0.5025688

63857.302

0.9637104

4.00E-04

1132.3015

225328

3.7554667

0.9696439

0.0029834

0.2413307

0.0102346

0.2061994

0.0353675

0.5075742

80150.191

0.9662254

3.00E-04

1408.1156

280231

4.6705167

0.9747033

0.00291

0.1759618

1.33E-04

0.3669061

0.1257354

0.3317159

113404.32

0.9705993

2.00E-04

1971.5276

392334

6.5389

0.9766492

0.0027735

0.0301947

6.71E-05

0.5176071

0.1508071

0.3015366

178704.5

0.9755657

1.00E-04

3079.9296

612906

10.2151

0.9807356

0.0020734

0.0352193

6.16E-05

0.5728769

0.1558284

0.2362122

189645.84

0.9762081

9.00E-05

3289.3618

654583

10.909717

0.9801518

0.0017323

0.0301881

5.37E-05

0.5326786

0.1708962

0.2663572

199240.38

0.9767577

8.00E-05

3124.5779

621799

10.363317

0.980541

0.0016933

0.0201314

4.96E-05

0.5176013

0.1909908

0.2713782

213000.2

0.9770862

7.00E-05

3870.0804

770149

12.835817

0.9820977

0.0017903

0.0201276

4.13E-05

0.5377

0.1608375

0.2814242

232538.81

0.9775898

6.00E-05

4183.5427

832531

13.875517

0.9819031

0.0019222

0.0251499

3.54E-05

0.4321747

0.2914793

0.2512723

261837.84

0.9784054

5.00E-05

4671.7035

929680

15.494667

0.9824869

0.0017131

0.020118

0.0050529

0.4673476

0.2864494

0.2211226

293045.84

0.97917

4.00E-05

4496.6231

894833

14.913883

0.982876

0.0017905

0.0150892

2.13E-05

0.5125703

0.206044

0.266342

341946.9

0.9802202

3.00E-05

5834.7286

1161121

19.352017

0.9836544

0.0016258

8.67E-06

0.0050394

0.467342

0.2964908

0.2311632

408835.39

0.9810798

2.00E-05

6995.1508

1392042

23.2007

0.9846274

0.0016328

4.22E-06

7.36E-06

0.2663364

0.4673396

0.2663348

576604.23

0.9824663

1.00E-05

9819.1457

1954028

32.567133

0.9856003

0.0014906

0.005029

6.68E-06

0.3567873

0.3718623

0.266335

590518.09

0.9824595

9.00E-06

10070.03

2003949

33.39915

0.9861841

0.0016341

3.66E-06

6.13E-06

0.361812

0.4221129

0.2160835

609672.87

0.9826296

8.00E-06

10578.678

2105158

35.085967

0.9854057

0.0014217

0.0100532

5.28E-06

0.3517614

0.4321629

0.206033

649084.43

0.9828379

7.00E-06

11378.653

2264389

37.739817

0.9863787

0.0014723

2.51E-06

4.55E-06

0.3919619

0.402012

0.2060328

688141.75

0.9829699

6.00E-06

11112.593

2211411

36.85685

0.9863787

0.0013737

0.0050274

3.74E-06

0.366836

0.3919614

0.2361828

739405.14

0.983187

5.00E-06

13885.628

2763247

46.054117

0.9863787

0.0013701

0.0050268

2.85E-06

0.3165845

0.4221118

0.2562828

814895.43

0.9833523

4.00E-06

12441.407

2475855

41.26425

0.9875462

0.0013463

0.0100515

2.26E-06

0.3115589

0.4221114

0.2562826

898370.47

0.983451

3.00E-06

15068.241

2998588

49.976467

0.9867679

0.0012352

0.0100511

0.0050265

0.3065335

0.4422116

0.2361817

1018724.4

0.9834647

2.00E-06

17163.116

3415468

56.924467

0.9865733

0.0014891

0.0100506

6.75E-07

0.2462316

0.4422113

0.3015079

1244358.3

0.9834852

1.00E-06

20607.568

4100909

68.348483

0.9865733

0.001324

0.0100506

6.44E-07

0.3216084

0.4522616

0.2160808

1291161.7

0.9834999

9.00E-07

21746.186

4327501

72.125017

0.987157

0.0014341

0.0050255

5.71E-07

0.2512566

0.432161

0.311558

1360011.7

0.9835537

8.00E-07

22496.085

4476721

74.612017

0.9867679

0.0014877

0.0050254

4.83E-07

0.2412064

0.432161

0.3216083

1402576.1

0.9834344

7.00E-07

24104.799

4796856

79.9476

0.9865733

0.0014402

0.0100505

4.13E-07

0.3015078

0.4371861

0.2512565

1430741.6

0.9834246

6.00E-07

24127.779

4801430

80.023833

0.987157

0.0014815

0.0050253

0.0100506

0.3366836

0.3718594

0.2763821

1539160.9

0.9834148

5.00E-07

26017.894

5177575

86.292917

0.9867679

0.0013904

0.0100504

2.66E-07

0.2964825

0.4170855

0.2763821

1618461.8

0.983409

4.00E-07

27559.96

5484442

91.407367

0.9867679

0.001473

0.0100504

2.00E-07

0.2864323

0.4020101

0.3015076

1702883.1

0.9833728

3.00E-07

29320.739

5834845

97.247417

0.9867679

0.0013969

0.0150755

1.47E-07

0.2663317

0.4221106

0.2964825

1843820.1

0.9831616

2.00E-07

31024.427

6173862

102.8977

0.9865733

0.0013638

0.0050252

0.0050252

0.2763819

0.3919598

0.3216081

2188509.1

0.9828672

1.00E-07

37078.025

7378528

122.97547

0.98813

0.0015414

0.0150754

0.0100503

0.2914573

0.3517588

0.3316583

2266508.3

0.9827519

9.00E-08

38511.402

7663774

127.72957

0.9875462

0.0015187

0.0201005

5.58E-08

0.2964824

0.3567839

0.3266332

2273906.5

0.9828144

8.00E-08

38618.528

7685090

128.08483

0.9861841

0.0014832

0.0100503

4.94E-08

0.2713568

0.3969849

0.3216081

2310469.9

0.9827157

7.00E-08

39082.382

7777409

129.62348

0.9867679

0.0014673

0.0150754

0.0100503

0.2512563

0.3668342

0.3567839

2424313.6

0.9827822

6.00E-08

42822.03

8521589

142.02648

0.9863787

0.0015439

 

 

這張圖是δ=5e-5到δ=6e-8的pave曲線,相當直觀當δ=8e-7時網絡達到峯值,峯值是0.983554。

這張圖是δ=1e-5到δ=6e-8的pave曲線,表明對三層網絡收斂標準是有最優值的,超過最優值以後網絡性能是下降的。

《估算卷積核數量的近似方法》實驗表明卷積核數量是有最優值的

《平均分辨準確率對網絡隱藏層節點數的非線性變化關係03》實驗表明隱藏層節點數是有最優值的。

因爲有最優值的存在,如果將網絡的收斂標準設定爲某一迭代次數,則將迭代次數調大並不必然導致網絡的性能改善。如將收斂標準設爲6e-8,平均性能只有峯值δ=8e-7的0.999216.但迭代次數卻是峯值的1.78倍,耗時是峯值的1.9倍,也就是用了1.9倍的時間卻換來性能下降萬分之8.或者也可以解釋成導致網絡性能下降的一個原因恰恰是迭代次數過多了。

 

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